Problem: Simplify. Remove all perfect squares from inside the square root. Assume $x$ is positive. $\sqrt{20x^8}=$
Explanation: Factor $20$ and find the greatest perfect square: $20=2\cdot 2\cdot 5=2^2\cdot 5$ Find the greatest perfect square in $x^8$ : $x^8=\left(x^4\right)^2$ $\begin{aligned} \sqrt{20x^8}&=\sqrt{2^2\cdot 5\cdot \left(x^4\right)^2} \\\\ &=\sqrt{2^2}\cdot \sqrt{5} \cdot \sqrt{\left(x^4\right)^2} \\\\ &=2\cdot \sqrt{5} \cdot x^4 \\\\ &=2x^4\sqrt{5} \end{aligned}$